TSTP Solution File: CSR037+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CSR037+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 21:41:11 EDT 2023
% Result : Theorem 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : CSR037+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 11:41:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.48
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 Take the following subset of the input axioms:
% 0.21/0.49 fof(just12, axiom, mtvisible(c_tptpgeo_member7_mt) => geographicalsubregions(c_georegion_l2_x5_y8, c_georegion_l3_x15_y24)).
% 0.21/0.49 fof(just13, axiom, mtvisible(c_tptpgeo_member7_mt) => geographicalsubregions(c_georegion_l3_x15_y24, c_georegion_l4_x45_y72)).
% 0.21/0.49 fof(just34, axiom, ![X, Y, Z]: ((geographicalsubregions(X, Y) & geographicalsubregions(Y, Z)) => geographicalsubregions(X, Z))).
% 0.21/0.49 fof(query37, conjecture, mtvisible(c_tptpgeo_member7_mt) => geographicalsubregions(c_georegion_l2_x5_y8, c_georegion_l4_x45_y72)).
% 0.21/0.49
% 0.21/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.49 fresh(y, y, x1...xn) = u
% 0.21/0.49 C => fresh(s, t, x1...xn) = v
% 0.21/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.49 variables of u and v.
% 0.21/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.49 input problem has no model of domain size 1).
% 0.21/0.49
% 0.21/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.49
% 0.21/0.49 Axiom 1 (query37): mtvisible(c_tptpgeo_member7_mt) = true2.
% 0.21/0.49 Axiom 2 (just13): fresh66(X, X) = true2.
% 0.21/0.49 Axiom 3 (just12): fresh65(X, X) = true2.
% 0.21/0.49 Axiom 4 (just13): fresh66(mtvisible(c_tptpgeo_member7_mt), true2) = geographicalsubregions(c_georegion_l3_x15_y24, c_georegion_l4_x45_y72).
% 0.21/0.49 Axiom 5 (just12): fresh65(mtvisible(c_tptpgeo_member7_mt), true2) = geographicalsubregions(c_georegion_l2_x5_y8, c_georegion_l3_x15_y24).
% 0.21/0.49 Axiom 6 (just34): fresh38(X, X, Y, Z) = true2.
% 0.21/0.49 Axiom 7 (just34): fresh39(X, X, Y, Z, W) = geographicalsubregions(Y, W).
% 0.21/0.49 Axiom 8 (just34): fresh39(geographicalsubregions(X, Y), true2, Z, X, Y) = fresh38(geographicalsubregions(Z, X), true2, Z, Y).
% 0.21/0.49
% 0.21/0.49 Goal 1 (query37_1): geographicalsubregions(c_georegion_l2_x5_y8, c_georegion_l4_x45_y72) = true2.
% 0.21/0.49 Proof:
% 0.21/0.49 geographicalsubregions(c_georegion_l2_x5_y8, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 7 (just34) R->L }
% 0.21/0.49 fresh39(true2, true2, c_georegion_l2_x5_y8, c_georegion_l3_x15_y24, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 2 (just13) R->L }
% 0.21/0.49 fresh39(fresh66(true2, true2), true2, c_georegion_l2_x5_y8, c_georegion_l3_x15_y24, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 1 (query37) R->L }
% 0.21/0.49 fresh39(fresh66(mtvisible(c_tptpgeo_member7_mt), true2), true2, c_georegion_l2_x5_y8, c_georegion_l3_x15_y24, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 4 (just13) }
% 0.21/0.49 fresh39(geographicalsubregions(c_georegion_l3_x15_y24, c_georegion_l4_x45_y72), true2, c_georegion_l2_x5_y8, c_georegion_l3_x15_y24, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 8 (just34) }
% 0.21/0.49 fresh38(geographicalsubregions(c_georegion_l2_x5_y8, c_georegion_l3_x15_y24), true2, c_georegion_l2_x5_y8, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 5 (just12) R->L }
% 0.21/0.49 fresh38(fresh65(mtvisible(c_tptpgeo_member7_mt), true2), true2, c_georegion_l2_x5_y8, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 1 (query37) }
% 0.21/0.49 fresh38(fresh65(true2, true2), true2, c_georegion_l2_x5_y8, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 3 (just12) }
% 0.21/0.49 fresh38(true2, true2, c_georegion_l2_x5_y8, c_georegion_l4_x45_y72)
% 0.21/0.49 = { by axiom 6 (just34) }
% 0.21/0.49 true2
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49
% 0.21/0.49 RESULT: Theorem (the conjecture is true).
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